Forced, nonlinear, planar and nonplanar oscillations of a cantilvered beam including static deflection

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dc.contributor.authorShyu, In-Ming Kevinen
dc.contributor.committeecochairMook, Dean T.en
dc.contributor.committeecochairPlaut, Raymond H.en
dc.contributor.committeememberHendricks, Scott L.en
dc.contributor.committeememberGrant, John W.en
dc.contributor.committeememberKlaus, Martinen
dc.contributor.departmentEngineering Mechanicsen
dc.date.accessioned2014-03-14T21:14:28Zen
dc.date.adate2008-06-06en
dc.date.available2014-03-14T21:14:28Zen
dc.date.issued1991en
dc.date.rdate2008-06-06en
dc.date.sdate2008-06-06en
dc.description.abstractIn this dissertation, the response of a slender, elastic, cantilevered beam to a simple harmonic excitation is investigated. The effects of nonlinear curvature, nonlinear inertia, viscous damping and static load are included. The nonlinear equations governing the motion of the beam are derived by the Lagrangian approach. The deflections are expressed as expansions in terms of the linear free-vibration modes. Galerkin’s method is used to eliminate the spatial functions from the governing equations. Three modes are used in this procedure. Approximate solutions of the temporal equations are determined by the method of multiple scales. Four first-order ordinary differential equations govern the amplitudes and phases, and predict a whirling motion under certain situations. The solutions of the modulation equations can be fixed points, limit cycles or chaotic motions. Previous studies considered whirling produced by a primary resonance. In this dissertation, secondary resonances are considered in addition to primary resonance. Previous derivations of equations of motion contain only the linear and cubic terms without consideration of the static displacement produced by the weight of the beam. As a result of this static deflection, there are quadratic terms in the governing equations which introduce the possibility of a superharmonic resonance of order two and a subharmonic resonance of order two. It is shown that out-of-plane motion is possible in every resonance when the principal moments of inertia of the beam cross-section are approximately equal. The longer the beam is, the more prominent the whirling motion becomes. If the excitation frequency is increased or decreased through a resonance, for most cases, the non-stationary response from the method of multiple scales shows good agreement with that from the original differential equations.en
dc.description.degreePh. D.en
dc.format.extentxvii, 269 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06062008-171257en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06062008-171257/en
dc.identifier.urihttp://hdl.handle.net/10919/38461en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1991.S549.pdfen
dc.relation.isformatofOCLC# 25140740en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1991.S549en
dc.subject.lcshGirders -- Testingen
dc.titleForced, nonlinear, planar and nonplanar oscillations of a cantilvered beam including static deflectionen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineEngineering Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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